Computer Science and Mathematics

Abstract: In real-world decision-making, constructing mathematical models is often difficult because the data are incomplete, uncertain, or even contradictory. The neutrosophic refined set provides a robust and flexible approach for effectively handling and representing these types of uncertainties. Various studies have highlighted its significant applications in decision making. In this study, a power mean operator is introduced to aggregate multiple Neutrosophic Refined Sets (NRSs) into a Single-Valued Neutrosophic Set (SVNs). The core mathematical properties of the newly introduced neutrosophic refined power mean operator are established. Moreover, two categories of neutrosophic refined cross-entropy measures are presented: one adapted from the SVNs-cross-entropy measure, and the other specifically formulated for neutrosophic refined sets. By employing the defined measures, an innovative decision making strategy is developed under the neutrosophic refined set environment. To demonstrate the effectiveness and practical relevance of the grounded strategy a numerical example based on the selection of an educational stream is solved.

Abstract: Software as a Service (SaaS) has become a key enabler of digital transformation and e-government modernization through scalable, flexible, and cost-effective service delivery. However, evidence of SaaS adoption in Southern African Development Community (SADC) public sectors remains limited and uneven. This study systematically reviews literature published between 2015 and 2025 on SaaS adoption, digital readiness, infrastructure, policy environments, and institutional capacity across SADC member states. Using PRISMA-guided screening, 31 studies were synthesized through narrative thematic analysis informed by the Technology–Organisation–Environment (TOE) framework and Institutional Theory. The findings reveal significant disparities in SaaS readiness across the region. South Africa is the only country with substantial empirical evidence of public-sector SaaS adoption, while most member states demonstrate only indirect indicators of readiness, including ICT maturity and e-government development. Four major barriers were identified: infrastructure deficits, policy and regulatory fragmentation, institutional capacity constraints, and uneven regional readiness. The study also identifies a “readiness paradox,” whereby stricter data sovereignty regulations co-exist with inadequate infrastructure for compliant SaaS deployment. The study contributes a contextualized framework for sustainable SaaS adoption in SADC public sectors.

Abstract: With the increasing penetration of wind power, the uncertainty of wind power generation poses greater challenges to the secure operation of power grids. This paper proposes WindPower-SAFusion, an improved Informer-based model for wind power forecasting. The proposed model optimizes long-sequence modeling from three aspects. First, ProbSparse self-attention is adopted to reduce the computational complexity from O(L2) to O(LlogL). Second, a convolutional distillation encoder is introduced to compress the input sequence and highlight key temporal features. Third, a multivariate fusion and recursive multi-step forecasting framework is constructed. Using historical power and wind speed information, experiments are conducted on measured data from the Daliang Wind Farm in Guazhou, Gansu Province, China. The results show that the proposed model significantly outperforms several mainstream forecasting models in 1-day, 3-day, and 7-day forecasting tasks. Ablation experiments further demonstrate that each core module plays a critical role in improving forecasting accuracy and generalization performance. Therefore, the proposed method provides a technically feasible solution with promising engineering application potential for power grid dispatching and wind power management.

Abstract: The rapid growth of Internet of Things (IoT) ecosystems has significantly increased cybersecurity threats due to device heterogeneity, resource limitations, and exposure to distributed attacks. Although Federated Learning (FL) has emerged as a promising privacy-preserving machine learning paradigm for decentralized intrusion detection, existing FL approaches often suffer from non-independent and identically distributed (non-IID) data, communication inefficiency, adversarial attacks, and unstable convergence in heterogeneous IoT environments. This study proposes a Privacy-Enhanced Federated Learning (PEFL) framework for adaptive and secure intrusion detection in large-scale IoT networks. The framework integrated differential privacy, secure aggregation, adaptive client selection, trust-aware federated optimization, and edge-assisted hierarchical coordination to improve robustness, scalability, and communication efficiency. The framework was evaluated using benchmark cybersecurity datasets, including CICIDS2017, UNSW-NB15, TON_IoT, and Bot-IoT under heterogeneous and adversarial conditions. Experimental results established that the proposed PEFL framework achieved improved intrusion detection accuracy, faster convergence stability, enhanced resilience against poisoning attacks, and reduced communication overhead compared with conventional FL approaches such as FedAvg and FedProx. The findings further indicated that adaptive client selection and trust-aware aggregation significantly improve model reliability and robustness in resource-constrained IoT environments. This framework will contribute toward the development of scalable, privacy-preserving, and deployable federated intrusion detection systems for next-generation intelligent IoT infrastructures.

Abstract: The paper shows how the ideas of Archimedes about integrating “mechanical methods” and formal reasoning can be connected with the modern-day use of three computer programs – Wolfram Alpha, Maple, and Excel – in exploring topics from elementary theory of numbers. Explorations deal with subsequences of integer sequences through step-by-step elimination of every other term obtained on the previous step. This process, resembling the sieve of Eratosthenes, is applied to tetrahedral numbers appearing in the social context of the family therapy triangulation method. It is demonstrated that symbolic computations of Wolfram Alpha enable generalization in the construction of the sieves that is confirmed by Maple and a spreadsheet. The paper addresses one of the aims of the special issue by demonstrating the duality of mathematics and technology in the sense that whereas the latter facilitates new approaches to knowledge acquisition, the former can be used to improve the efficiency of computations by reflecting on the results made possible by those approaches. The activities advocate for the value of integrating ancient ideas, digital tools, and elementary number theory in the education of mathematics teachers. Reflective comments by teacher candidates are included as appropriate.

Abstract: This paper presents a comprehensive cross-era analysis of the algorithmic evolution of Large Language Models (LLMs) through four developmental epochs: Before Transformer (pre-2017), Transformer (post-2017), Instruction-tuned \& Open-source LLMs, and Multimodal Agents (2024-2025). A novel innovation pathway framework is introduced that traces causal relationships between architectural breakthroughs and emergent capabilities, addressing critical research gaps in three dimensions: (1) Cross-paradigm synthesis connecting statistical foundations to modern multimodal systems, (2) Causal innovation mapping demonstrating how architectural choices propagate through model generations, and (3) Cross-domain capability analysis quantifying transfer between representation learning, knowledge acquisition, behavioral alignment, and multimodal integration. This analysis reveals that LLM progression represents fundamental paradigm shifts rather than incremental improvements, with transformer architectures, human feedback mechanisms, and open-source ecosystems collectively enabling the transition from specialized NLP tools to general reasoning systems. We provide empirical evidence through case studies of capability emergence, quantify innovation impacts using performance metrics, and examine safety implications through recent jailbreak analysis and refusal mechanism studies. The contributions include: (a) a unified lifecycle synthesis with original analytical framework, (b) innovation trajectory mapping with causal pathway analysis, and (c) validated evolutionary principles for forecasting next-generation AI capabilities.

Abstract: Road traffic accidents pose a growing public safety challenge in rapidly urbanizing regions of Nigeria, where infrastructure development and traffic management often lag behind increasing vehicle use. This study investigates the spatial distribution and hotspot patterns of road traffic accidents in Jega Local Government Area, Kebbi State, Nigeria, using Inverse Distance Weighting (IDW) spatial interpolation. Georeferenced accident count data were analyzed through descriptive statistics, spatial visualization, and interpolation on a 200 × 200 grid with an edge buffer to minimize boundary effects. Accident hotspots were delineated using an 80th percentile threshold of interpolated intensity values. The results reveal a strongly clustered spatial structure, characterized by pronounced inequality in accident occurrence, where a small number of locations account for a disproportionate share of recorded accidents. IDW surfaces, contour maps, three-dimensional visualizations, and Google Earth-compatible outputs consistently identify high-risk zones around major junctions and traffic convergence areas. The findings demonstrate that IDW provides a transparent, computationally efficient, and operationally effective approach for accident hotspot identification in data-constrained urban settings. The study offers practical decision-support tools for targeted road safety interventions and contributes to evidence-based traffic management planning in developing urban environments.

Abstract: This paper proposes a decentralized data trading approach based on the Automated Market Maker (AMM) mechanism, aiming to break through the bottlenecks in data trading efficiency and fairness via the collaborative innovation of market-oriented pricing mechanisms and automated trading processes. We focus on constructing an automatic pricing and matching mechanism based on liquidity pools. Subsequently, mathematical modeling and simulations reveal slippage generation mechanisms in data liquidity pools under trading shocks and imbalances. To address these issues, a novel dual slippage optimization mechanism integrating dynamic trade splitting and alternating order sorting is proposed, which decomposes orders into sub-orders and reorganizes their timing, establishing a dynamic equilibrium model. Experiments show the method reduces average slippage amplitude from 2.1% to 0.5% and representing a 76.2% reduction, significantly enhancing price stability and market efficiency. This research explores the mechanism of applying AMM to data asset trading and overcomes AMM's limitations, providing a theoretical and empirical foundation for building low-cost, high-fairness data trading systems through mechanism innovation and technical optimization.

Abstract: Cybersecurity risk is commonly expressed through impact and likelihood, yet likelihood remains difficult to estimate because cyber incidents are underreported, heterogeneous datasets are weakly comparable, and attacker behaviour changes faster than conventional probability baselines. This article proposes a method for operationalising likelihood through a cyber-exposure profile that integrates external cyber knowledge and organisation-specific telemetry into a graph-based representation. The contribution is a formally specified artefact chain — from unified data model through organization-specific profiling, metric registry, likelihood scoring, and control prioritization — that operationalises four constructs grounded in incident evidence: exposure, traceability, motivation, and Systems Update. The pipeline provides a pathway from heterogeneous source evidence to a bounded likelihood indicator comparable across organizations and observation periods. An evaluation in 15 real organizations shows that those implementing the cyber-exposure profile were associated with reduced incident frequency and faster detection-and-response times, providing preliminary empirical support for the framework’s directional claims.

Abstract: While Large Language Models (LLMs) have shown great promise in transforming credit risk assess-ment, existing evaluation frameworks are almost exclusively concerned with general financial NLP tasks and neglect the specific reasoning needed by practitioners. To address this, we develop the Credit Context Log Understanding and Prediction Evaluation (CCLUPE) benchmark. Unlike the previous benchmarks, CCLUPE aims to capture and evaluate the intricate reasoning unique to each constituent of the Chinese credit market, where evaluations are heavily based on the integration and synthesis of complex transacted logs and the prediction of hidden financial behaviors. Unlike previous benchmarks, CCLUPE aims to capture and evaluate the intricate reasoning unique to each constituent of the Chinese credit market. Unlike previous benchmarks, CCLUPE aims to capture and evaluate the intricate reasoning unique to each constituent. CCLUPE boasts more than 4,000 premium samples segmented by individual and micro-enterprise customers and distributed among 7 principal log types and 16 sub log types. A comprehensive assessment process involving upwards of 20 professional annotators is enacted to guarantee the quality of the dataset. Moreover, we introduce Log-Score, a novel evaluation metric designed to incorporate log misunderstanding penalties and assess multifaceted competencies. Even the state-of-the-art models underperform when it comes to these high-stakes tasks. CCLUPE serves as a rigorous testbed for the next generation of financial LLMs, ensuring their robustness for deployment in complex real credit scenarios.

Abstract: We develop a metamathematical analogue of special and curved relativity built from exact witness architectures. For a proposition equipped with exact positive and negative witness channels, the corresponding positive and negative terminal directions are promoted to formal terminal meta-fibers. These play the role of null directions and generate a terminal cone together with an invariant interval dσ² = dU dV = dT² − dX². This yields a flat theory, Terminal-Fiber Relativity, in which Lorentz-type transformations arise as exactly the observer changes preserving the terminal interval and the oriented terminal cone. We then reinterpret the principal barrier theorems of exact witness architecture theory as relativistic laws: the Selection Jump Theorem becomes a universal null-propagation principle; reflection collapse forbids global internal inertial charts on Π₁-universal sectors; and Tarski and diagonal barriers forbid global arithmetic charts on truth-universal sectors. The second half of the paper extends the flat theory to curved meta-relativity. We define terminal-fiber manifolds, local null charts, occupancy fields, barrier fields, and a scalar curvature law in dimension 1+1. Because ordinary Einstein dynamics is trivial in two dimensions, the curved theory is governed instead by a conformal scalar equation sourced by barrier density and mixed terminal occupancy. We also formulate a higher-rank extension and a functorial packaging from exact witness architectures to terminal-fiber geometries. The result is not an empirical substitute for spacetime physics, but a geometric invariant theory of exact recognition.

Abstract: Generative molecular models such as diffusion models and graph neural networks are widely used in drug design. However, their black-box nature means they lack an explicit understanding of chemical rules (e.g., valency, charge, aromaticity), often generating chemically impossible structures such as pentavalent carbon. To address this issue, this paper proposes Atomic-SCS, an atom-level chemical rule scoring tool based on a symbolic approach. Atomic-SCS does not rely on data-driven training but directly applies IUPAC rules to independently score each atom across four dimensions: valency, charge, aromaticity, and ring strain. It outputs continuous scores (0 = fully compliant, 1 = severe violation), provides atom-level diagnostic reports, and generates prioritized repair suggestions sorted by severity. The tool supports three strictness levels (conservative, balanced, liberal) and three operation modes (assess, diagnose, repair), and can be accessed via a command-line interface or Python API. Validation on 100 normal and 100 problematic molecules shows that Atomic-SCS effectively distinguishes valid from invalid structures (Mann-Whitney U test, p < 1e-18). The scoring functions are continuous and can serve as reward signals in generative model training. On a standard CPU, scoring 100 molecules averaged 0.000071 s per molecule. This work provides a rule-based scoring tool for generative molecular design.

Abstract: In recent years, wearable sensing technologies have been widely used for motion analysis in sports; however, in kendo, motion evaluation still largely relies on subjective assessment, and quantitative approaches remain limited. This study proposes an embedded Inertial Measurement Unit (IMU) based sensing system for motion analysis of kendo swings. The system integrates a compact IMU and a microcontroller within the handle of a bamboo sword (shinai), enabling unobtrusive measurement without affecting usability. To achieve robust orientation estimation under highly dynamic conditions, an error-state Kalman filter (ESKF) is applied using only 6-axis IMU data, without relying on magnetometer measurements. This enables stable gravity compensation and reliable extraction of motion-related acceleration components. Experimental results showed that experienced practitioners exhibited significantly higher peak acceleration (p = 0.002) and smaller peak width (p = 0.022) than novices, indicating sharper and more efficient motion. No significant difference was observed in the secondary peak ratio. These results demonstrate that the proposed system can quantitatively capture kendo motion characteristics and distinguish practitioners of different proficiency, highlighting the effectiveness of magnetometer-free IMU-based motion analysis for highly dynamic movements.

Abstract: Traditional evaluation of language models prioritizes Ñnal-answer accuracy, offering limited insight into the reasoning processes that produce those outputs. Thispaper introduces a formal framework for evaluating reasoning integrity by modelinginference as a trajectory of belief states under uncertainty. We deÑne externallyobservable belief states that capture hypotheses, uncertainty distributions, and con-straints at each reasoning step, enabling analysis without reliance on internal modelrepresentations. Building on this formulation, we propose a divergence functional that quantiÑessustained disagreement between reasoning trajectories, together with a complexityregularization term that penalizes excessive or redundant reasoning. These compo-nents are combined into a uniÑed scoring function that balances consistency andparsimony. To operationalize the framework, we introduce a multi-stage evalua-tion protocol that constrains intermediate reasoning, injects minimal adversarialperturbations, and measures both divergence and repair cost. We establish theoretical properties of the proposed metrics, including bound-edness, invariance under semantic-preserving transformations, and stability undercontrolled perturbations. Analytical examples illustrate how the framework distin-guishes robust reasoning processes from brittle or superÑcial ones that maintaincorrectness without internal consistency. By shifting evaluation from outcomes tothe dynamics of reasoning, this framework provides a principled basis for assessingreliability and stability in modern language models.

Abstract: A cover-based notion of topological sensitivity and sensitivity at a point is introduced, which is the same as the popular concept of sensitivity in metric spaces. The basin of attraction of infinity, the point of compactification of locally compact, non-compact topological spaces, is studied in this paper. It is proved that, under certain conditions on the underlying map f , the set of points whose orbits have compact support, the basin of attraction of infinity, and the set of sensitive points are identical, thus generalizing the standard Julia sets on the Riemann sphere.

Abstract: Intraoperative hypotension (IOH) is a critical complication during surgical procedures that can lead to severe adverse outcomes including myocardial injury, acute kidney injury, and increased mortality. Early prediction of hypotensive events remains a significant challenge in perioperative medicine. This study leverages the Medical Informatics Operating Room Vitals and Events Repository (MOVER) dataset, a comprehensive collection of intraoperative physiological signals and clinical events, to develop and evaluate machine learning models for predicting hypotensive events 5, 10, and 15 minutes before onset.The MOVER dataset contains high-frequency vital sign measurements including heart rate, blood pressure, oxygen saturation, and respiratory metrics from over 5,000 surgical procedures. Extensive preprocessing and feature engineering were performed to extract statistical, temporal, and interaction features across multiple time windows. Multiple machine learning algorithms were implemented and compared including XGBoost, Random Forest, Histogram-based Gradient Boosting (HGB), Support Vector Machines (SVM) with RBF kernel, Long Short-Term Memory (LSTM) networks, Multilayer Perceptron (MLP), and K-Nearest Neighbors (KNN).Experimental results demonstrate that XGBoost achieves the highest predictive performance with an accuracy of 94.2%, precision of 93.8%, recall of 94.5%, and AUC-ROC of 0.973 for 5-minute prediction windows. Performance remained strong for 10-minute (AUC-ROC = 0.942) and 15-minute (AUC-ROC = 0.908) predictions. Feature importance analysis revealed that mean arterial pressure (MAP) trends, heart rate variability, shock index, and time since last vasopressor administration were the most significant predictors. Error analysis identified borderline MAP values and rapid hemodynamic changes as primary sources of misclassification.The proposed models demonstrate strong potential for real-time clinical decision support systems to alert anesthesiologists of impending hypotensive events, enabling proactive interventions and improved patient outcomes. This research represents the first comprehensive comparison of multiple machine learning algorithms on the MOVER dataset for hypotension prediction, providing a foundation for future clinical implementation and prospective validation studies.

Abstract: We propose that the first four non-trivial zeros of the Riemann zeta function satisfy the exact relation \(8\pi^2(\gamma_4/\gamma_1)^2 = 366\), equivalently \(\gamma_4/\gamma_1 = \sqrt{183}/(2\pi)\). This relation emerges from three fundamental considerations: (1) the geometric framework of the Riemann-Möbius-Enneper (RME) triad, (2) the constructive interference condition derived from the pendulum-zeta isomorphism with harmonic parameter \(k=3\), and (3) the self-consistency condition \(K_g \cdot C = 1\) where \(K_g\) and \(C\) are explicit functions of the zeros. We further explore a connection to modular forms, noting that the ratio \(\gamma_4/\gamma_1\) equals the ratio of logarithms of the Dedekind eta function evaluated at the Heegner points \(\tau_{163} = (1 + i\sqrt{163})/2\) and \(\tau_{43} = (1 + i\sqrt{43})/2\). The numbers 163 and 43 are the two largest Heegner numbers, famously associated with Ramanujan's observation that \(e^{\pi\sqrt{163}}\) is almost an integer. Where Ramanujan found striking approximations, we find exact equalities — transforming near-integer phenomena into precise identities that link the zeros of the zeta function to modular forms and, through the geometric framework, to fundamental physical constants. This connection reveals that the identity \(8\pi^2(\gamma_4/\gamma_1)^2 = 366\) is equivalent to a profound relation between these special values of the eta function. Numerical verification with 200+ digit precision confirms the exact nature of all identities. This result would provide a mathematical foundation for the geometric origin of fundamental physical constants, including the fine-structure constant \(\alpha^{-1}=137.035999084\), the Planck length \(\ell_P = 1.616255\times 10^{-35}\,\text{m}\), and the hydrogen Lamb shift correction \(\Delta\nu_{\text{Lamb}} = 7.314\,\text{kHz}\).

Abstract: City-scale, in-the-wild Augmented Reality (AR) learning paths must remain operable under Bring Your Own Device (BYOD) heterogeneity, outdoor tracking degradation, public-space safety, and interruption recovery. This study conceptualizes the Art Nouveau Path as an AR learning service and makes a theoretical contribution by proposing a Determinant-driven Requirements traceability model that treats implementation Determinants as Requirements signals and links them to testable Requirements, transfer Artefacts, and evidence anchors for replication. Methods combined 8 Points of Interest (POIs) and 36 tasks profiling, group-session logs (118 sessions), and teacher-facing records from a validation workshop (T1-VAL, N=30) and in situ observation (T2-OBS, N=24). Teachers open-text fields were segmented into meaning units and coded with an eight-Determinant taxonomy, with intercoder reliability assessed on a stratified subset (Krippendorff’s alpha = 0.83). Logs and a post-path student questionnaire (S2-POST, N=439) bounded enactment feasibility and data integrity, without learning-outcome inference. Dominant determinants concerned onboarding and legibility, marker robustness and recovery, and curriculum framing, alongside safety and fallback constraints. These signals were translated into 18 “shall” Requirements with acceptance criteria and bidirectional trace links to transfer 6 Artefacts. The resulting transfer kit specifies routines, maintenance, incident handling, and fallback procedures to reduce replication fragility across teams.

Abstract: The transition from fifth-generation (5G) to sixth-generation (6G) mobile networks represents a fundamental shift in wireless communication paradigms, driven by the need for ultra-low latency, extreme data rates, native intelligence, and support for mission-critical and immersive applications. This paper presents the Rexhep Network Optimization Framework, a layered and AI-native architectural model designed to enable a smooth, efficient, and scalable evolution from 5G to 6G systems. The proposed framework integrates physical and spectrum intelligence, intelligent radio access networks (RAN) with edge computing, virtualized core networks with network slicing, and AI-driven optimization and control mechanisms. It further incorporates advanced service layers supporting extended reality (XR), digital twins, AI-based security, and mission-critical services. The framework explicitly addresses the coexistence of 5G and 6G technologies through phased deployment, hybrid optimization, and dynamic spectrum management, ensuring backward compatibility while enabling 6G-dominant capabilities. By positioning artificial intelligence as a cross-layer enabler rather than an auxiliary function, the proposed framework provides a systematic approach for network automation, resilience, and performance optimization in next-generation communication ecosystems. The presented model offers a conceptual foundation for future research, standardization, and practical deployment strategies toward 6G networks.

Abstract: This study proposes a Natural Language Processing (NLP)-based evaluation framework to examine the linguistic consistency of Large Language Model (LLM)-generated personalized texts over time. NLP metrics were used to quantify and compare linguistic patterns across repeated generations produced using identical prompts. In Experiment 1, internal reliability was examined across 10 repeated generations from four LLMs (Claude, Llama, Gemini, and ChatGPT) applied to 10 scientific texts tailored for a specific reader profile. Linear mixed-effects models showed no effect of repeated generation on linguistic features (e.g., cohesion, syntactic complexity, lexical sophistication), suggesting short-term consistency across repeatedly generated outputs. Experiment 2 examined linguistic variation across model updates of GPT-4o (October 2024 vs. June 2025) and GPT-4.1 (June 2025). Significant variations were observed across outputs from different model versions. GPT-4o (June 2025) generated more concise but cohesive texts, whereas GPT-4.1 (June 2025) generated outputs that are more academic, lexically sophisticated and complex syntax. Given the rapid evolution of LLMs and the lack of standardized methods for tracking output consistency, the current work demonstrates one of the applications of NLP-based evaluation approaches for monitoring meaningful linguistic shifts across model updates over time.